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UBC Theses and Dissertations

Multivariate one-sided tests for multivariate normal and nonlinear mixed effects models with complete and incomplete data Wang, Tao


Multivariate one-sided hypotheses testing problems arise frequently in practice. Various tests haven been developed for multivariate normal data. However only limited literatures are available for multivariate one-sided testing problems in regression models. In particular, one-sided tests for nonlinear mixed effects (NLME) models, which are popular in many longitudinal studies, have not been studied yet, even in the cases of complete data. In practice, there are often missing values in multivariate data and longitudinal data. In this case, standard testing procedures based on complete data may not be applicable or may perform poorly if the observations that contain missing data are discarded. In this thesis, we propose testing methods for multivariate one-sided testing problems in multivariate normal distributions with missing data and for NLME models with complete and incomplete data. In the missing data case, testing methods are based on multiple imputations. Some theoretical results are presented. The proposed methods are evaluated using simulations. Real data examples are presented to illustrate the methods.

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